Parliament will stop the UK crashing out of the EU without any Brexit deal, even if MPs block Theresa May’s deal, Amber Rudd has said, suggesting the prime minister’s threat of “no Brexit” was more likely than no deal.

The work and pensions secretary told Conservative rebels considering voting against the prime minister’s final deal that “Brexiters may lose their Brexit” and said new amendments that they would like even less could be put down if the deal was rejected.

“I think what the country needs now is the certainty of an orderly exit,” she told BBC Radio 4’s Today programme.

Asked whether the alternative choice was no deal or a second referendum, Rudd said: “It is my view that parliament, the House of Commons, will stop no deal. There is not a majority in the House of Commons to allow that to take place.”

Her comments appeared to contradict the prime minister’s repeated assertion that crashing out of the EU with no deal was the biggest risk of any rebellion, a persuasion tactic used on some wavering Labour MPs.

However, Rudd’s comments were backed by another minister, Liz Truss, later on Wednesday, suggesting it was a co-ordinated tactic to convince Brexiters.

The chief secretary to the Treasury said this was “a historic opportunity to leave the EU” which could be put at risk. “If my colleagues don’t vote for this in parliament, we are in serious danger of not leaving at all,” she told BBC Radio 5 Live.

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“I am very, very worried about what the alternative looks like, because I’m a democrat and I believe people voted in good faith to leave the EU and we need to deliver that.”

The shadow Brexit secretary, Keir Starmer, has used the same argument as Rudd to make the opposite case – that MPs can safely vote down May’s deal because parliament will stop a no-deal exit. Starmer said Rudd’s comments made clear that deal or no deal was now a “false choice”.

“Amber Rudd seems to have ignored the No 10 spin by admitting that parliament would stop a no-deal Brexit,” Starmer said. “If the prime minister’s deal is rejected then MPs will not sit back and allow us to crash out of the EU without an agreement. Parliament will take back control.”

Her comments were also backed by the Tory MP Damian Collins, who has said he would vote against the deal as it stood, saying he believed an election or a second referendum were on the table if the deal fell. “There isn’t a majority in the House of Commons to allow [no deal] to take place,” he said.

Rudd said she also viewed a second referendum as unlikely. “I think people will take a careful look over the abyss from all parties and consider what they think is in the best interest of the whole country,” she said.

Rudd’s comments came as May prepared to head to Brussels on Wednesday afternoon for talks with the European commission president, Jean-Claude Juncker. Downing Street sources have said the meeting is not for the leaders to sign off an agreement, but is part of the ongoing negotiations.

The EU’s deputy chief negotiator, Sabine Weyand, told ambassadors for the member states on Tuesday evening that negotiations on the political declaration had stalled on the issues of Gibraltar, the demands from the European fishing industry for access to British waters, and the UK’s hopes to link the language on the trade in goods to the Chequers proposals and “frictionless trade”.

It is understood that the issue of Spain’s demands for a veto on Gibraltar’s inclusion in a future trade deal will probably be settled only during May’s meeting with Juncker. The two other outstanding issues are to be the subject of negotiations at the level of officials on Wednesday morning.

EU diplomats said it was likely that the issue of fisheries would have to be settled through a side-declaration to the main document in which the 27 would make their demands for a continuation of the status quo without it being jointly agreed with the British government and causing a political bombshell at home.

The diplomats said the British government would have to accept weaker language than a commitment to “frictionless trade” in the document, given the decision to leave the single market and customs union along with the jurisdiction of the European court of justice.

Elmar Brok, a German centre-right politician who sits on the European parliament’s steering group, said he was “quite optimistic” about a resolution on Spain’s problems with Gibraltar.

“The Gibraltar question will be solved with goodwill on all sides,” he said, suggesting it was political play. “Britain tortured Spain a lot when Spain wanted to become a member of the European Union on the Gibraltar question and the Spanish remember.”

He warned British politicians hoping to rewrite the withdrawal treaty that no better offer would be made. If the British parliament rejected the deal “then it is over”, he said. “That’s the deal, buy it. This is a joint deal accepted by the British government ... There will be no better deal.”

May will arrive in Brussels bolstered by the failure of her critics to summon enough letters of discontent with her leadership in order to force a confidence vote – but more than enough MPs have stated they will vote against her deal in parliament to block it.

Speaking to the Bundestag on Wednesday morning, the German chancellor, Angela Merkel, said her country was ready to agree to Britain’s exit agreement with the EU, despite misgivings over how to solve the Irish backstop issue. “We know how difficult the discussions are in Britain, but I can say for Germany that we will agree to this exit agreement,” she said.

“There is still an objection to it in Spain – I can’t say how precisely we will solve this but I hope it will be solved by Sunday,” she added.

Repeating her oft-stated claim that her administration regretted Britain’s decision to leave but fully respected the democratic process behind it, Merkel stressed that Germany intended to continue cooperation with Britain. “We want – and that is in our fundamental interests to do so – to have a good relationship with Britain in the future as well.”

She admitted that the issue of the Irish backstop continued to be highly problematic and would be “very, very difficult to solve”.

“I think, rightly, we have placed value on Britain not being able to decide unilaterally when it ends the custom union, rather that Britain should, together with the EU define this date and only after that the future relationship comes into effect,” she said.

Rudd said she believed some colleagues could be won over on the provisions in the backstop customs arrangement, which she said was there only until technology was ready to allow for a frictionless border on the island of Ireland. Her comments were similar to a persuasion tactic No 10 has used on would-be rebels in recent days.

“It is obviously the practical approach to have, but I understand some colleagues are concerned,” she said.